# Improved Pose Graph Optimization for Planar Motions Using Riemannian Geometry on the Manifold of Dual Quaternions

## TL;DR

This paper introduces a Riemannian geometry-based method for planar pose graph optimization that inherently considers the nonlinear SE(2) group structure, leading to improved convergence robustness over existing methods.

## Contribution

It proposes a novel Riemannian pose graph optimizer (RPG-Opt) using dual quaternions and exponential retraction, enhancing robustness in large uncertainty scenarios.

## Key findings

- Achieves equivalent accuracy to state-of-the-art methods.
- Demonstrates better convergence robustness under large odometry uncertainties.
- Validated on public planar pose graph datasets.

## Abstract

We present a novel Riemannian approach for planar pose graph optimization problems. By formulating the cost function based on the Riemannian metric on the manifold of dual quaternions representing planar motions, the nonlinear structure of the SE(2) group is inherently considered. To solve the on-manifold least squares problem, a Riemannian Gauss-Newton method using the exponential retraction is applied. The proposed Riemannian pose graph optimizer (RPG-Opt) is further evaluated based on public planar pose graph data sets. Compared with state-of-the-art frameworks, the proposed method gives equivalent accuracy and better convergence robustness under large uncertainties of odometry measurements.